Least-squares reverse-time migration yields better images than the conventional reverse time migration. However, images of least-squares reverse-time migration may still contain significant artifacts for sparse seismic data when source/receiver intervals are too large. We develop a novel least-squares reverse-time migration method with compressive sensing to improve migration imaging with sparse seismic data. Our method incorporates an Lp-norm-based compressive sensing term in the objective function of least-squares reverse-time migration. We employ an alternating-minimization algorithm to solve the optimization problem of our new least-squares reverse-time migration method. We validate our new method using synthetic vertical seismic profiling (VSP) data from a geophysical model built using geologic features and well log data at the Raft River geothermal field. We apply our method to synthetic VSP data for a sparse source array and compare the results with those obtained with a dense source array. Our new migration method produces an image using a sparse source array with image quality similar to that obtained using a dense source array.

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